Because of the increased size of databases, computer processing of sequence data requires efficient algorithms. Probably the most frequently used algorithms are variants of the Needleman-Wunsch algorithm, used to align and compare two sequences. Comparison of more than two sequences is a problem of current interest, but this is even more computationally expensive. A theory relating alignment efficiencies and inequalities directly was used to develop several "new" algorithms, which were then tested empirically on the Laboratory mini-computer. One of these was shown to have a clear superiority in both time and memory requirements and is the fastest known algorithm for aligning two sequences under Needleman-Wunsch single indel weight penalties. Similar new algorithms allowing multiple indel penalties (which are biologically more realistic) were also tested and one was shown to be the best alignment algorithm under multiple indel weights currently available. The theory is also applicable to multiple sequence alignment.